Problem: Simplify the following expression: $t = \dfrac{k^2 - 9k + 14}{k - 7} $
Answer: First factor the polynomial in the numerator. $ k^2 - 9k + 14 = (k - 7)(k - 2) $ So we can rewrite the expression as: $t = \dfrac{(k - 7)(k - 2)}{k - 7} $ We can divide the numerator and denominator by $(k - 7)$ on condition that $k \neq 7$ Therefore $t = k - 2; k \neq 7$